{"id":251431,"date":"2022-09-10T10:40:19","date_gmt":"2022-09-10T05:10:19","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/six-charges-are-placed-at-the-vertices-of-a-regular-hexagon-as-shown-in-the-figure-the-electric-field-on-the-line-passing-through-point-o-and-perpendicular-to-the-plane-of-the-figure-as-a-function-of\/"},"modified":"2022-09-10T10:40:19","modified_gmt":"2022-09-10T05:10:19","slug":"six-charges-are-placed-at-the-vertices-of-a-regular-hexagon-as-shown-in-the-figure-the-electric-field-on-the-line-passing-through-point-o-and-perpendicular-to-the-plane-of-the-figure-as-a-function-of","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/six-charges-are-placed-at-the-vertices-of-a-regular-hexagon\/","title":{"rendered":"Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (assume x >>a)"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (assume x >>a)","custom_permalink":"question\/physics\/six-charges-are-placed-at-the-vertices-of-a-regular-hexagon\/"},"categories":[],"acf":{"question":"

Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (assume x >>a)<\/p>

<\/figure>","options":[{"option":"

0<\/p>","correct":false},{"option":"

Qa<\/mi>\u03c0\u03b5<\/mi>0<\/mn><\/msub>x<\/mi>3<\/mn><\/msup><\/mrow><\/mfrac><\/math><\/p>","correct":true},{"option":"

2<\/mn>Qa<\/mi><\/mrow>\u03c0\u03b5<\/mi>0<\/mn><\/msub>x<\/mi>3<\/mn><\/msup><\/mrow><\/mfrac><\/math><\/p>","correct":false},{"option":"

3<\/mn><\/msqrt>Qa<\/mi><\/mrow>\u03c0\u03b5<\/mi>0<\/mn><\/msub>x<\/mi>3<\/mn><\/msup><\/mrow><\/mfrac><\/math><\/p>","correct":false}],"solution":"

Two opposite charges situated at opposite vertices forms a dipole and point lies on bisector line of dipole for one dipole.<\/p>

<\/figure>

E<\/mi>\u2192<\/mo><\/mover>=<\/mo>\u2212<\/mo>K<\/mi>p<\/mi>\u2192<\/mo><\/mover><\/mrow>x<\/mi>3<\/mn><\/msup><\/mfrac><\/math><\/p>

Direction of field due to these three dipoles is in a horizontal plane at distance x from plane of hexagon and parallel to it, mutually having angle 60\u00b0 with each other.<\/p>

E<\/mi>0<\/mn><\/msub>=<\/mo>E<\/mi>+<\/mo>E<\/mi>=<\/mo>2<\/mn>E<\/mi>=<\/mo>2<\/mn>Q<\/mi>(<\/mo>2<\/mn>a<\/mi>)<\/mo><\/mrow>4<\/mn>\u03c0\u03b5<\/mi>0<\/mn><\/msub>\u22c5<\/mo>x<\/mi>3<\/mn><\/msup><\/mrow><\/mfrac>=<\/mo>Qa<\/mi>\u03c0\u03b5<\/mi>0<\/mn><\/msub>x<\/mi>3<\/mn><\/msup><\/mrow><\/mfrac><\/math><\/p>
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